Lexicographically largest sub-sequence of the given string

Given a string str containing lowercase characters, the task is to find the lexicographically largest sub-sequence of str.

Examples:

Input: str = “abc”
Output: c
All possible sub-sequences are “a”, “ab”, “ac”, “b”, “bc” and “c”
and “c” is the largest among them (lexicographically)

Input: str = “geeksforgeeks”
Output: ss

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: Let mx be the lexicographically largest character in the string. Since we want the lexicographically largest sub-sequence we should include all occurrences of mx. Now after all the occurrences have been used, the same process can be repeated for the remaining string (i.e. sub-string after the last occurrence of mx) and so on until the there are no more characters left.

Below is the implementation of the above approach:

C++

// C++ implementation of the approach 
#include <bits/stdc++.h> 
using namespace std; 
  
// Function to return the lexicographically 
// largest sub-sequence of s 
string getSubSeq(string s, int n) 
{ 
    string res = ""; 
    int cr = 0; 
    while (cr < n) { 
  
        // Get the max character from the string 
        char mx = s[cr]; 
        for (int i = cr + 1; i < n; i++) 
            mx = max(mx, s[i]); 
        int lst = cr; 
  
        // Use all the occurrences of the 
        // current maximum character 
        for (int i = cr; i < n; i++) 
            if (s[i] == mx) { 
                res += s[i]; 
                lst = i; 
            } 
  
        // Repeat the steps for the remaining string 
        cr = lst + 1; 
    } 
    return res; 
} 
  
// Driver code 
int main() 
{ 
    string s = "geeksforgeeks"; 
    int n = s.length(); 
    cout << getSubSeq(s, n); 
} 

Java

// Java implementation of the approach 
class GFG 
{ 
  
    // Function to return the lexicographically 
    // largest sub-sequence of s 
    static String getSubSeq(String s, int n) 
    { 
        String res = ""; 
        int cr = 0; 
        while (cr < n)  
        { 
  
            // Get the max character from the String 
            char mx = s.charAt(cr); 
            for (int i = cr + 1; i < n; i++) 
            { 
                mx = (char) Math.max(mx, s.charAt(i)); 
            } 
            int lst = cr; 
  
            // Use all the occurrences of the 
            // current maximum character 
            for (int i = cr; i < n; i++)  
            { 
                if (s.charAt(i) == mx)  
                { 
                    res += s.charAt(i); 
                    lst = i; 
                } 
            } 
  
            // Repeat the steps for  
            // the remaining String 
            cr = lst + 1; 
        } 
        return res; 
    } 
  
    // Driver code 
    public static void main(String[] args)  
    { 
        String s = "geeksforgeeks"; 
        int n = s.length(); 
        System.out.println(getSubSeq(s, n)); 
    } 
} 
  
// This code is contributed by Rajput-Ji 

Python3

# Python 3 implementation of the approach 
  
# Function to return the lexicographically 
# largest sub-sequence of s 
def getSubSeq(s, n): 
    res = "" 
    cr = 0
    while (cr < n): 
          
        # Get the max character from  
        # the string 
        mx = s[cr] 
        for i in range(cr + 1, n): 
            mx = max(mx, s[i]) 
        lst = cr 
  
        # Use all the occurrences of the 
        # current maximum character 
        for i in range(cr,n): 
            if (s[i] == mx): 
                res += s[i] 
                lst = i 
  
        # Repeat the steps for the  
        # remaining string 
        cr = lst + 1
      
    return res 
  
# Driver code 
if __name__ == '__main__': 
    s = "geeksforgeeks"
    n = len(s) 
    print(getSubSeq(s, n)) 
  
# This code is contributed by 
# Surendra_Gangwar 

C#

// C# implementation of the approach  
using System; 
  
class GFG  
{  
  
    // Function to return the lexicographically  
    // largest sub-sequence of s  
    static String getSubSeq(String s, int n)  
    {  
        String res = "";  
        int cr = 0;  
        while (cr < n)  
        {  
  
            // Get the max character from  
            // the String  
            char mx = s[cr];  
            for (int i = cr + 1; i < n; i++)  
            {  
                mx = (char) Math.Max(mx, s[i]);  
            }  
            int lst = cr;  
  
            // Use all the occurrences of the  
            // current maximum character  
            for (int i = cr; i < n; i++)  
            {  
                if (s[i] == mx)  
                {  
                    res += s[i];  
                    lst = i;  
                }  
            }  
  
            // Repeat the steps for  
            // the remaining String  
            cr = lst + 1;  
        }  
        return res;  
    }  
  
    // Driver code  
    public static void Main(String[] args)  
    {  
        String s = "geeksforgeeks";  
        int n = s.Length;  
        Console.WriteLine(getSubSeq(s, n));  
    }  
}  
  
// This code is contributed by 29AjayKumar 

PHP

<?php 
// PHP implementation of the approach 
  
// Function to return the lexicographically 
// largest sub-sequence of s 
function getSubSeq($s, $n) 
{ 
    $res = ""; 
    $cr = 0; 
    while ($cr < $n)  
    { 
  
        // Get the max character from the string 
        $mx = $s[$cr]; 
        for ($i = $cr + 1; $i < $n; $i++) 
            $mx = max($mx, $s[$i]); 
        $lst = $cr; 
  
        // Use all the occurrences of the 
        // current maximum character 
        for ($i = $cr; $i < $n; $i++) 
            if ($s[$i] == $mx)  
            { 
                $res .= $s[$i]; 
                $lst = $i; 
            } 
  
        // Repeat the steps for the 
        // remaining string 
        $cr = $lst + 1; 
    } 
    return $res; 
} 
  
// Driver code 
$s = "geeksforgeeks"; 
$n = strlen($s); 
echo getSubSeq($s, $n); 
  
// This code is contributed by  
// Akanksha Rai 
?> 

Output:

ss

Time Complexity: O(N) where N is the length of the string.

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My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

PHP

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